MIMO Networks
The use of multiple antennas in multi-input, multi-output (MIMO) networks can dramatically increase data throughput. In rich-scattering channel environments, the channel capacity increases linearly according to min(M, N), where M and N denote the number of transmit antennas and receive antennas, respectively. To achieve such capacity gains, accurate channel state information (CSI) is necessary for coherent communications.
CSI
Without CSI, there is non-coherent communications. For non-coherent channels, the capacity becomes a function of M′(1−M′/L) in high signal-to-noise ratio (SNR) environments, where M′=min(M,N, └L/2┘), and L denotes the coherence time (or, the length of a non-coherent codeword), where └.┘ is the floor function.
Non-coherent codes include unitary space-time constellations, exponential mapping Grassmann codes, non-parametric Grassmann codes, and differential space-time modulations. Unitary space-time codes asymptotically achieve the non-coherent channel capacity for high SNRs. For such codes, optimal performance of maximum-likelihood decoding can be attained by using a generalized likelihood ratio test (GLRT) receiver, without having the CSI.
GLRT
The GLRT receiver uses implicit channel state estimation for each codeword of the non-coherent codes at the time of decoding. However, the performance of the conventional GLRT receiver degrades seriously when the channel coherence time is much shorter than the lengths of the non-coherent codes L. This constrains the code length to be reasonably short in practice. Shorter space-time codes in turn decrease the capacity gains for M′(1−M′/L).